As has already been pointed out multiple times there should have been no need to change anything. The phone is none the wiser which ISP, EE or BT is supplying the connection and neither is the BT hub. The phone should have connect to the BT hub by its self when the broadband started.
The phone would not have selected the EEWifi signal which caused the EEWifi logon web page to open, that would have required human intervention to have made the connection and then enter the details.
I suspect that for what ever reason the the OP is not following everything that has already been suggested and that there is user error when trying to connect and as such I will now bow out of this thread.
